Continuous geometry

In mathematics, continuous geometry is an analogue of complex projective geometry introduced by von Neumann (1936, 1998), where instead of the dimension of a subspace being in a discrete set ${\displaystyle 0,1,\dots ,{\textit {n}}}$, it can be an element of the unit interval ${\displaystyle [0,1]}$. Von Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the hyperfinite type II factor.